Two stacks can be efficiently implemented using one fixed sized array: stack #1 starts from the left end and grows to the right, and stack #2 starts from the right end and grows to the left. Is the ...

Suppose you have sets $S_1, \dots S_m$ such that $\sum_i |S_i| = n$. The goal is to arrange all the sets into a (possible unconnected) DAG such that $S_i$ is a parent (or ancestor) of $S_j$ iff $S_j \...

Has anyone studied the asymptotics of problems in complexity classes like $BPP$? The thought came to me that if a problem in $BPP$ only requires $O(log(n))$ bits of entropy to solve then, intuitively, ...

It is believed showing $BPP$ in $P$ involves good $PRG$s and faces lower bound barriers.
Does showing $BPP$ in $P^{NP}$ which would mean $BPP\neq EXP^{NP}$ face similar $PRG$ and give lower bounds?
...

I am reading Alon et al.'s paper Linear Circuits over $GF(2)$ and I am having trouble seeing the counting argument showing that most matrices need a circuit of size $\Omega(n^2/\log n)$. This result ...

We have n balls where 1 is a little heavier than the others and we want to find that heavier ball. We can only put some balls on one side of the scale and some on the other side and see if it leans ...

Termination is the following problem.
Input: a Petri Net with initial marking
Output: "yes" iff there exists an infinite firing sequence. The naive algorithm in the case of bounded nets for example ...

To the best of my knowledge, it is known that $NEXP^{NP} \nsubseteq P/poly$, but it's still not known if $NEXP \nsubseteq P/poly$.
For more info, see "Superpolynomial circuits, almost sparse oracles ...

If I'm not mistaken it is not known whether $E^{NP} \subseteq {\rm SIZE}(n)$
where $E^{NP}$ is the class of problems solvable by a TM which works in time $2^{O(n)}$ and is allowed to make queries of ...

Suppose you have developed an upper bound on the number of vertices of a particular graph. This bound is the best possible bound that can be found for any given instance. What do you call such a bound?...

Suppose you have a $K$ armed stochastic bandit problem but with full information. There are $K$ arms with mean rewards $\mu_1,...,\mu_K$. At each step we have to select an arm, collect the reward from ...

An addition chain of size $n$ for given integers $n_1,n_2\dots ,n_p$ is a sequence of integers $k_1,k_2\dots ,k_n$ such that
$k_1=1$,
for all $i$ $(2\le i\le m)$ we have $k_i=k_j+k_m$ for some $1\le ...

The halting problem is well-known to be uncomputable. However, it is possible to exponentially "compress" information about the halting problem, so that decompressing it is computable.
More precisely,...

In general determinants have many identities. Would it help the $GCT$ program by invoking the paradigm of identities such as to state that if the permanent is converted to determinant then it has to ...

I would like to lower bound the quantity $\Pr[X\ge t, Y\ge t]=\Pr[\min(X,Y)\ge t]$ using the small moments of $X$, $Y$ and $XY$.
In particular I am interested in the case where $E[X]=E[Y]=0$, but $E[X ...

Are there lowerbounds known for representing the Tribes function by a circuit consisting of a single layer of polynomial threshold gates feeding into maybe a trivial summing gate? (Even for degree $1$ ...

Consider an $n \times n \times n$ cube. I would like to consider subsets of points in the cube with the two following constraints:
Each row in the cube (in any of the three directions) has exactly 2 ...

Let's consider following variation of $k$-SAT that I will call $k$-partite $k$-SAT:
given $n$ variables that are divided into $k$ groups and a $k$-SAT formula $\phi$ such that each clause has literal ...

The title is somewhat "arrogant": say, most of us treat $P\neq NP$ as an "obvious" fact, albeit no proof is in sight. But my question is at a much, much lower level, is about a fact which "should be" ...

Natural proofs paper shows 'if there is a natural property not possessed by any function in P/poly then there is no $2^{n^\epsilon}$-hard PRG'.
Is it easy to see the converse 'if there is no $2^{n^\...

Subgraph isomorphism problem is a well studied problem: given graphs $G$ and $H$, one needs to answer if $H$ contains $G$ as a subgraph. It was proven that this problem requires $|H|^{\theta(|G|)}$ ...

Consider $S_1, ...,S_n \subseteq [U]$ where size of $U$ is polylogarithmic in $n$. We allow infinite time to pre-process these sets and then ask queries of the form $S_i \cap S_j$ is empty or not. We ...

Let $X$ be a set of $n$-bit Boolean functions of the form $f:\{0,1\}^n\rightarrow \{0,1\}$. For instance, $X$ could be the set of $n$-bit monotone Boolean functions, or the set of $n$-bit functions ...

Assume we know a parameter $n\in\mathbb N$, and then get to observe a sequence of elements $x_1,\ldots, x_n$, one at a time.
Our goal is to count the number of distinct elements in $x_1,\ldots, x_n$, ...